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University of Cambridge > Talks.cam > Special DPMMS Colloquium > Random Surfaces and Quantum Loewner Evolution

## Random Surfaces and Quantum Loewner EvolutionAdd to your list(s) Download to your calendar using vCal - Jason Miller (MIT)
- Thursday 30 January 2014, 13:15-14:00
- CMS, MR5.
If you have a question about this talk, please contact HoD Secretary, DPMMS. This talk has been canceled/deleted What is the canonical way to choose a random, discrete, two-dimensional manifold which is homeomorphic to the sphere? One procedure for doing so is to choose uniformly among the set of surfaces which can be generated by gluing together $n$ Euclidean squares along their boundary segments in such a way that the resulting surface is homeomorphic to the sphere. This is an example of what is called a random planar map and is a model of what is known as pure discrete quantum gravity. The asymptotic behavior of these discrete, random surfaces has been the focus of a large body of literature in both probability and combinatorics. This has culminated with the recent works of Le Gall and Miermont which prove that the $n \to \infty$ distributional limit of these surfaces exists with respect to the Gromov-Hausdorff metric after appropriate rescaling. The limiting random metric space is called the Brownian map. Another canonical way to choose a random, two-dimensional manifold is what is known as Liouville quantum gravity (LQG). This is a theory of continuum quantum gravity introduced by Polyakov to model the time-space trajectory of a string. Its metric when parameterized by isothermal coordinates is formally described by $e In this talk, I will describe a new family of growth processes called quantum Loewner evolution (QLE) which we propose using to endow LQG with a distance function which is isometric to the Brownian map. I will also explain how QLE is related to DLA , the dielectric breakdown model, and SLE . Based on joint works with Scott Sheffield. This talk is part of the Special DPMMS Colloquium series. ## This talk is included in these lists:This talk is not included in any other list Note that ex-directory lists are not shown. |
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